Simplify the following expression: $\dfrac{63x^5}{14x^5}$ You can assume $x \neq 0$.
Solution: $ \dfrac{63x^5}{14x^5} = \dfrac{63}{14} \cdot \dfrac{x^5}{x^5} $ To simplify $\frac{63}{14}$ , find the greatest common factor (GCD) of $63$ and $14$ $63 = 3 \cdot 3 \cdot 7$ $14 = 2 \cdot 7$ $ \mbox{GCD}(63, 14) = 7 $ $ \dfrac{63}{14} \cdot \dfrac{x^5}{x^5} = \dfrac{7 \cdot 9}{7 \cdot 2} \cdot \dfrac{x^5}{x^5} $ $\phantom{ \dfrac{63}{14} \cdot \dfrac{5}{5}} = \dfrac{9}{2} \cdot \dfrac{x^5}{x^5} $ $ \dfrac{x^5}{x^5} = \dfrac{x \cdot x \cdot x \cdot x \cdot x}{x \cdot x \cdot x \cdot x \cdot x} = 1 $ $ \dfrac{9}{2} \cdot 1 = \dfrac{9}{2} $